Download presentation

Presentation is loading. Please wait.

Published byMiya Broadnax Modified over 3 years ago

1
Chapter 2 Describing Contingency Tables Reported by Liu Qi

2
Review of Chapter 1 Categorical variable Response-Explanatory variable Nominal-Ordinal-Interval variable Continuous-Discrete variable Quantitative-Qualitative variable

3
Review(cont.) Use binomial, multinomial and Poisson distribution Not normality distribution Tow most used models: logistic regression(logit) log linear

4
Binomial distribution

5
Multinomial distribution

6
Poisson distribution

7
Poisson Multinomial

8
Something unfamiliar Maximum likelihood estimation Confidence intervals Statistical inference for binomial parameters multinomial parameters ……

9
Terminology and notation Cell Contingency table

10
Terminology and notation Subjective Sensitivity and Specificity Conditional distribution Joint distribution Marginal distribution Independence =>

11
Sampling Scheme Poisson the joint probability mass function: Multinomial independent/product multinomial Hyper geometric

12
Example for sampling

13
Types of studies Retrospective: case-control Prospective: – Clinical trial observational study – Cohort study Cross-sectional: experimental study

14
Comparing two proportions Difference Relative risk Odds ratio – Odds defined as – For a 2*2 table, odds ratio – Another name: cross-product ratio

15
Properties of the Odds Ratio 0=<θ <, θ=1 means independence of X and Y the farther from 1.0, the stronger the association between X and Y. log θ is convenient and symmetric Suitable for all direction No change when any row/column multiplied by a constant.

16
Aspirin and Heart Attacks Revisited 189/11034=0.0171 104/11037=0.0094 Relative risk: 0.0171/0.0094=1.82 Odds ratio: (189*10933)/(10845*1 04)=1.83

17
Case-Control Studies and the Odds Ratio

18
However(cont.)

19
Partial association in stratified 2*2 tables Experimental studies We hold other covariates constant to study the effect of X on Y. Observational studies Control for a possibly confounding variable Z Partial tables=>conditional association Marginal table

20
Death penalty example

21
Death penalty example(cont.)

22
Simpsons paradox

23
Conditional and marginal odds ratios Conditional Marginal

24
Conditional independence Conditional independence: Joint probability:

25
Marginal independence

26
Marginal versus Conditional

27
Marginal versus Conditional(cont.) Marginal conditional

28
Homogeneous Association For a 2*2*K table, homogeneous XY association defined as: A symmetric property: – Applies to any pair of variables viewed across the categories of the third. – No interaction between two variables in their effects on the other variable.

29
Homogeneous Association(cont.) Suppose: – X=smoking(yes, no) – Y=lung cancer(yes, no) – Z=age( 65) – And Age is an Effect Modifier

30
Extensions for i*j Tables For a 2*2 table Odds ratio An i*j table Odds ratios

31
Representation methods Method 1

32
Method 2

33
For I*J tables (I-1)*(J-1) odds ratios describe any association All 1.0s means INDEPENDENCE! Three-way I*J*K tables, Homogeneous XY association means: any conditional odds ratio formed using two categories of X and Y each is the same at each category of Z.

34
Measures of Association Two kinds of variables: – Nominal variables – Ordinal variables Nominal variables: Set a measure for X and Y: – V(Y),V(Y|X) Proportional reduction:

35
Measures of variation Entropy: Goodman and Kruskal(1954) (tau) Lambda:

36
About Entropy Uncertainty coefficient: U=0=>INDEPENDENCE U=1=>π(j|i)=1 for each i, some j. Drawbacks: No intuition for such a proportional reduction.

37
Ordinal Trends An example:

38
Three kinds of relationship Concordant Discordant Tied

39
Example(cont.) D=849 Define (C-D)/(C+D) as Gamma measure. Here, A weak tendency for job satisfaction to increase as income increases.

40
Generalized

41
Properties of Gamma Measure Symmetric Range [-1,1] Absolute value of 1 means perfect linear Monotonicity is required for Independence =>,not vice-versa.

Similar presentations

OK

NORMAL OR GAUSSIAN DISTRIBUTION Chapter 5. General Normal Distribution Two parameter distribution with a pdf given by:

NORMAL OR GAUSSIAN DISTRIBUTION Chapter 5. General Normal Distribution Two parameter distribution with a pdf given by:

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on life study of mathematician blaise Ppt on human nutrition and digestion test Ppt on new zealand culture and customs Ppt on isobars and isotopes of hydrogen Ppt on haunted places in india Ppt on force and pressure for class 9 Ppt on area of trapezium shape Ppt on solid dielectrics for hot Ppt on search engine working Ppt on islam and science